A couple of other programs to consider:
Harvard Kennedy School (esp faculty associated with the Belfer Center), MIT, Princeton WWS, Fletcher school, Ohio State Mershon Center, Texas A&M. If you're open to a British-style PhD, the Kings College London War Studies or Defence Studies programs are excellent, and both offer blended distance learning--or if your personal situation allows, you could live in the UK for a few years. If you want to teach in the US. the UK programs may be less helpful, as many U.S. departments will look for some significant methodological (read: quantitative) background, which the British-style program won't provide. (You could offset that with a quant-intensive or mixed-methods dissertation that demonstrates mastery of the techniques--you just won't have classes to point to, since the British program is dissertation only).
The undergraduate GPA is certainly competitive. I don't know how the various schools would interpret the law school GPA but cum laude and published certainly help.
Since you have some time, I'd recommend doing some background reading on the faculty at the various schools (CV/major work) to get a sense of who you might be interested in working with. Then reach out to them and see how they assess your chances. While they may or may not be on the admissions committee, many will give you a sense of how your profile and interests fit with the school.